Existing　non-rigid　shape　matching　methods　mainly　involve　two　disadvantages.　(a)　Local　details　and　global　features　of　shapes　can　not　be　carefully　explored.　(b)　A　satisfactory　trade-off　between　the　matching　accuracy　and　computational　efficiency　can　be　hardly　achieved.　To　address　these　issues,　we　propose　a　local-global　commutative　preserving　functional　map　(LGCP)　for　shape　correspondence.　The　core　of　LGCP　involves　an　intra-segment　geometric　submodel　and　a　local-global　commutative　preserving　submodel,　which　accomplishes　the　segment-to-segment　matching　and　the　point-to-point　matching　tasks,　respectively.　The　first　submodel　consists　of　an　ICP　similarity　term　and　two　geometric　similarity　terms　which　guarantee　the　correct　correspondence　of　segments　of　two　shapes,　while　the　second　submodel　guarantees　the　bijectivity　of　the　correspondence　on　both　the　shape　level　and　the　segment　level.　Experimental　results　on　both　segment-to-segment　matching　and　point-to-point　matching　show　that,　LGCP　not　only　generate　quite　accurate　matching　results,　but　also　exhibit　a　satisfactory　portability　and　a　high　efficiency.　©　2021　ACM.